On the Equivalence of the Riemann-Liouville and the Caputo Fractional Order Derivatives in Modeling of Linear Viscoelastic Materials

Mathematics Subject Classification: 26A33

On the Zeros of the Solutions to Nonlinear Hyperbolic Equations with Delays

2002 Mathematics Subject Classification: Primary 35В05; Secondary 35L15

Measurement of the vascular input function in mice for DCE-MRI

DCE-MRI is an important technique in the study of small animal cancer models because its sensitivity to vascular changes opens the possibility of quantitative assessment of early therapeutic response. However, extraction of physiologically descriptive parameters from DCE-MRI data relies upon measurement of the vascular input function (VIF), which represents the contrast agent concentration time course in the blood plasma. This is difficult in small animal models due to artifacts associated with partial volume, inflow enhancement, and the limited temporal resolution achievable with MR imaging. In this work, the development of a suite of techniques for high temporal resolution, artifact resistant measurement of the VIF in mice is described. One obstacle in VIF measurement is inflow enhancement, which decreases the sensitivity of the MR signal to the presence of contrast agent. Because the traditional techniques used to suppress inflow enhancement degrade the achievable spatiotemporal resolution of the pulse sequence, improvements can be achieved by reducing the time required for the suppression. Thus, a novel RF pulse which provides spatial presaturation contemporaneously with the RF excitation was implemented and evaluated. This maximizes the achievable temporal resolution by removing the additional RF and gradient pulses typically required for suppression of inflow enhancement. A second challenge is achieving the temporal resolution required for accurate characterization of the VIF, which exceeds what can be achieved with conventional imaging techniques while maintaining adequate spatial resolution and tumor coverage. Thus, an anatomically constrained reconstruction strategy was developed that allows for sampling of the VIF at extremely high acceleration factors, permitting capture of the initial pass of the contrast agent in mice. Simulation, phantom, and in vivo validation of all components were performed. Finally, the two components were used to perform VIF measurement in the murine heart. An in vivo study of the VIF reproducibility was performed, and an improvement in the measured injection-to-injection variation was observed. This will lead to improvements in the reliability of quantitative DCE-MRI measurements and increase their sensitivity.

Fractional Calculus of the Generalized Wright Function

Mathematics Subject Classification: 26A33, 33C20.

Derivation of the probability distribution function for the local density of states of a disordered quantum wire via the replica trick and supersymmetry

We consider the statistical properties of the local density of states of a one-dimensional Dirac equation in the presence of various types of disorder with Gaussian white-noise distribution. It is shown how either the replica trick or supersymmetry can be used to calculate exactly all the moments of the local density of states.' Careful attention is paid to how the results change if the local density of states is averaged over atomic length scales. For both the replica trick and supersymmetry the problem is reduced to finding the ground state of a zero-dimensional Hamiltonian which is written solely in terms of a pair of coupled spins which are elements of u(1, 1). This ground state is explicitly found for the particular case of the Dirac equation corresponding to an infinite metallic quantum wire with a single conduction channel. The calculated moments of the local density of states agree with those found previously by Al'tshuler and Prigodin [Sov. Phys. JETP 68 (1989) 198] using a technique based on recursion relations for Feynman diagrams. (C) 2001 Elsevier Science B.V. All rights reserved.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

Study of the Myocardial Contraction and Relaxation Velocities through Doppler Tissue Imaging Echocardiography: A New Alternative in the Assessment of the Segmental Ventricular Function

OBJECTIVE: Doppler tissue imaging (DTI) enables the study of the velocity of contraction and relaxation of myocardial segments. We established standards for the peak velocity of the different myocardial segments of the left ventricle in systole and diastole, and correlated them with the electrocardiogram. METHODS: We studied 35 healthy individuals (27 were male) with ages ranging from 12 to 59 years (32.9 ± 10.6). Systolic and diastolic peak velocities were assessed by Doppler tissue imaging in 12 segments of the left ventricle, establishing their mean values and the temporal correlation with the cardiac cycle. RESULTS: The means (and standard deviation) of the peak velocities in the basal, medial, and apical regions (of the septal, anterior, lateral, and posterior left ventricle walls) were respectively, in cm/s, 7.35(1.64), 5.26(1.88), and 3.33(1.58) in systole and 10.56(2.34), 7.92(2.37), and 3.98(1.64) in diastole. The mean time in which systolic peak velocity was recorded was 131.59ms (±19.12ms), and diastolic was 459.18ms (±18.13ms) based on the peak of the R wave of the electrocardiogram. CONCLUSION: In healthy individuals, maximum left ventricle segment velocities decreased from the bases to the ventricular apex, with certain proportionality between contraction and relaxation (P<0.05). The use of Doppler tissue imaging may be very helpful in detecting early alterations in ventricular contraction and relaxation.

Dominance of positivity of the Green's function associated to a perturbed polyharmonic dirichlet boundary value problem by pointwise estimates

Magdeburg, Univ., Fak. für Mathematik, Diss., 2015

In defense of the "tunneling" wave function of the universe

The tunneling approach to the wave function of the Universe has been recently criticized by Bousso and Hawking who claim that it predicts a catastrophic instability of de Sitter space with respect to pair production of black holes. We show that this claim is unfounded. First, we argue that different horizon size regions in de Sitter space cannot be treated as independently created, as they contend. And second, the WKB tunneling wave function is not simply the inverse of the Hartle-Hawking one, except in very special cases. Applied to the related problem of pair production of massive particles, we argue that the tunneling wave function leads to a small constant production rate, and not to a catastrophe as the argument of Bousso and Hawking would suggest.

Analytic behavior of the QED polarizability function at finite temperature

We revisit the analytical properties of the static quasi-photon polarizability function for an electron gas at finite temperature, in connection with the existence of Friedel oscillations in the potential created by an impurity. In contrast with the zero temperature case, where the polarizability is an analytical function, except for the two branch cuts which are responsible for Friedel oscillations, at finite temperature the corresponding function is non analytical, in spite of becoming continuous everywhere on the complex plane. This effect produces, as a result, the survival of the oscillatory behavior of the potential. We calculate the potential at large distances, and relate the calculation to the non-analytical properties of the polarizability.

Organization and Coordination of the Highway Planning Function in Iowa, HR-150, 1971

The Engineering Research Institute at Iowa State University studied the organization and procedures for highway planning by all levels of government and the coordination among various state agencies and local governments in Iowa. Study information was derived from interviews, questionnaires, and a review of the literature. Representatives from state transportation or highway organizations in all states responded to questionnaires. Additionally, selected upper and intermediate level personnel from highway organizations in seven other states were interviewed and a visit was made to one state transportation department. Within Iowa, employees were interviewed in the Highway Commission, Office for Planning and Programming, Development Commission, Commerce Commission, Conservation Commission, and Highway Patrol. Nearly 600 officials of local governments in Iowa contributed factual data and opinions through questionnaires and interviews. Private citizens and consultants also provided input to the investigation through their responses to questionnaires. Twelve recommendations to improve highway planning in Iowa were formulated as a result of this study.

Spectral analysis of the angular distribution function of back reflectors for thin film silicon solar cells

Nowadays, one of the most important challenges to enhance the efficiency of thin film silicon solar cells is to increase the short circuit intensity by means of optical confinement methods, such as textured back-reflector structures. In this work, two possible textured structures to be used as back reflectors for n-i-p solar cells have been optically analyzed and compared to a smooth one by using a system which is able to measure the angular distribution function (ADF) of the scattered light in a wide spectral range (350-1000 nm). The accurate analysis of the ADF data corresponding to the reflector structures and to the μc-Si:H films deposited onto them allows the optical losses due to the reflector absorption and its effectiveness in increasing light absorption in the μc-Si:H layer, mainly at long wavelengths, to be quantified.